Students’ Strategies to Solve Reversible Problems of Function: The Part of Reversible Thinking

Abstract

This study aimed to reveal students’ strategies to solve reversible problems, particularly to function course. Individuals’ competence to solve reversible problems is the part of reversible thinking. This way of thinking refers to a reversible two-way relationship. Providing reversible problems is a way for teachers to develop their students’ reversible thinking. It was qualitative. 105 students who were prospective teachers of mathematics were selected as the subject of this study, and it took a test containing some reversible problems, such as function along with its graphic and between derivative and integral, as the instrument. The students’ results were further analyzed to reveal their strategies of solving those reversible problems. The finding showed that among 105 students, 62% of them were capable to draw the graph of an identified function through 4 different strategies, while 28% of them were capable to define the function of an identified graphic through 5 different strategies. The significant difference between those two percentages implied that only few students were capable to both drawing the graphic of an identified function and defining the function of an identified graphic. Overall, it indicated that the students were still less in constructing a reversible relationship between function and its graphic.

Reversible Thinking of Fifth Graders: Focus on Linier Equations

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“…When reversibility was considered as a feature of the development phase of one's cognition, it was definitely crucial. Relating to mathematics education, reversibility is a part of mathematical competence influencing students' successfulness in solving mathematics problems (Daulay et al, 2019;S. Maf'ulah & Juniati, 2019;Zandieh & Rasmussen, 2010).…”

“…Reversible thinking is defined as a primary grader's mental activity to make particular equations equivalent with the original one and then reverse them to the initial S. Maf'ulah & Juniati, 2019, 2020.…”

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